Sara,
If you have asthma, I am very glad that you are going to see your GP about this. I don't think it's time to give up vaping yet, but IF you are cleared to do so by your doc, may I suggest the following:
Different liquid delivery (I use MTL started with a Nautilus 2 tank which I was very pleased with, at loooow watts, like 7 or 8, with higher nic liquid.
I have asthma and various bronchial issues.... I was headed toward another pneumonia and decided to vape more and smoke less, and actually got worse. For me, it's PG that I'm sensitive to, but that may not be the case for you. I doubt that nicotine is your problem since you can smoke cigarettes, so going higher on nic is unlikely to cause these effects.
I would buy a small bottle of pure VG and nic (make sure the store can use a VG base for nic, if you are purchasing it) and a small bottle of PG and nic (same thing with the base). I'd start with the VG just because I'd think vaping PURE PG is going to be tough, but you can try it. AND ONLY if your doc clears you to do this, maybe with a rescue inhaler and/or nebulizer handy in case you get that bad reaction. Then try the VG, to see what that does. If neither causes problems, you know that 3 ingredients in your juice are safe/fine for you to use (or not! In which case you will be somewhat limited in your options/blends, but many people can make it work using greater or lesser percentages of one or the other. I stick to VG because I can make that work.
That leaves flavorings, which, given that the average employee in a vape store isn't going to be able to tell you every ingredient they use in every flavor.... Unless you get a quality vendor who might work with you on flavorings, you have the option of DIY-- I'd start with ONE flavor that you think you might like, and gradually and gently increase the percentage, and find a range of flavors that you can live with/enjoy.
I sympathize, I do have some allergies and sensitivities. Nothing like my kid though, and watching him gasp for air wasn't fun....
I do wonder if you could do allergy testing with an allergist on e-juice components and various flavors like they do with other things (pollens, etc.) and if that may be a definitive way to find out what you are allergic to without the "gasp for air" effect. I can't imagine it WOULDN'T be possible, and that might be a safer way to find out if you can a) find a doc and allergist who would go for that b) be up for possible cost, testing my son for allergies and treating them was NOT INEXPENSIVE but it greatly improved his quality of life, and I'm glad I did it (he was allergic to 19 things! 19 that he encountered daily!) and he hasn't used an inhaler since I can recall, once we completed his allergy regimen he didn't have any more symptoms at all, of course the process took 5 years and a LOT of prep for vacations, etc.
Okay. I'm going to stop. TL

R-- if you isolate ingredients/consult with doc/allergist, I believe you can make vaping work for you. I wouldn't use a sub0hm device, either. Doing all this has GOT to be safer than smoking, which is why I bothered to type all this out, especially if you have asthma. It may be more expensive and a pain at first, but I believe overall it will end up being worth it.
Take care and be safe!
Anna